The space of integration \(g^i\)  includes the orbits, i.e. the
subspaces defined by the gauge transformations of the metric field
(REF ). Since the action remains constant over any such
subspace, it is cleat that each of these subspaces contributes
infinite to the integral, which is, therefore, badly defined. Such
a divergence is similar to taking logarithm of determinant of a
degenerate matrix. This divergence it is a direct consequence of
the gauge invariance and represents the problem solved by the
DeWitt-Faddeev-Popov method [1]}, [2]}
in gravity and in the Yang-Mills theory (see also, e.g.,
[3]} for QG and further references in the
next Chapter [4]}).
